Three-dimensional slope stability analysis by elasto-plastic finite elements

Abstract

Slope stability analysis is one of the oldest applications in geotechnical engineering, yet it remains one of the most active areas of study in both research and practice. The vast majority of slope stability analyses are performed in two dimensions under the assumption of plane strain conditions. Even when two-dimensional (2D) conditions are not appropriate, three-dimensional (3D) analysis is rarely performed. There are a number of reasons for this. The majority of work on this subject strongly suggests that the 2D factor of safety is conservative (i.e. lower than the 'true' 3D factor of safety). Even when 3D may be justified on geometric grounds, the available methods, being often based on extrapolations of 2D 'methods of slices' to 3D 'methods of columns', are complex, involve numerous assumptions, and are not readily modified to account for realistic boundary conditions in the third dimension such as sloping abutments. The power and versatility of the elasto-plastic finite element approach to slope stability analysis in 2D are well known, and these advantages are even more attractive in 3D. The paper demonstrates some 3D slope stability analyses by finite elements, placing the results in context with 2D solutions and validating the results where possible against alternative methods. L'analyse de la stabilité des versants représente l'une des plus anciennes applications en ingénierie géotechnique. Elle reste pourtant l'une des disciplines d'étude les plus actives, en recherche et en pratique. La grande majorité des analyses de stabilité des versants est réalisée en deux dimensions, en considérant des conditions de déformation plane. Même lorsque des conditions à deux dimensions ne sont pas adaptées, il est rare que des analyses à trois dimensions soient effectuées, et ce pour un certain nombre de raisons. La majorité des travaux à ce sujet suggère fortement que le coefficient de sécurité 2D est conservateur (c'est-à-dire inférieur au « vrai » coefficient de sécurité 3D). Même lorsque des raisons géométriques justifieraient la 3D, les méthodes disponibles, souvent basées sur des extrapolations de « Méthode de coupes » 2D en « Méthode de colonnes » 3D, sont complexes, s'appuient sur de nombreuses hypothèses et ne peuvent être aisément modifiées pour tenir compte de conditions de frontière réalistes en 3D, telles que des culées inclinées. La puissance et la versatilité de l'approche des éléments finis en comportement élasto-plastique pour l'analyse de la stabilité des versants en 2D sont bien connues, et ces avantages sont encore plus prometteurs en 3D. Cet article présente certaines analyses de stabilité de versants en 3D en adoptant la méthode des éléments finis, mettant les résultats en contexte avec les solutions 2D et les validant contre des méthodes alternatives lorsqu'il est possible.

Arch Action Over an Excavated Pit on a Stable Scarp Investigated by Physical Model Tests

“…Despite the availability of threedimensional computer programs for analyzing deformation and stability in slopes, the calculations require many assumptions with regard to lateral forces, the initial stress distribution and other criteria of the critical slip surfaces which is sometimes lacking (Gri‹ths and Marquez, 2007;Loehr et al, 2004;Ugai and Leshchinsky, 1995;Wei et al, 2009). On the other hand, a two-dimensional analysis for the most critical cross-section will always lead to a conservative factor of safety; therefore, a three-dimensional analysis is not commonly employed for slope stability analyses.…”

On the reliability of earth slopes in three dimensions

“…The factor of safety in three dimension was always higher than in two dimension owing to side support, but tended to the plane strain solution for length ratios of the order of L/H > 10. It should be mentioned that Griffiths & Marquez (2007) used a mesh density similar to that shown in figure 3 but demonstrated that while finer meshes always gave slightly lower factors of safety than the coarser mesh, the difference never exceeded 2 per cent. …”

“…First, a conservative result will only be obtained if the most 'pessimistic' plane within a three-dimensional problem is selected for two-dimensional analysis. Griffiths & Marquez (2008) clearly showed planes within a three-dimensional slope that gave higher (unconservative) two-dimensional factors of safety than that of the full three-dimensional problem. In a slope that contains layering and strength variability in the out-of-plane direction, the choice of a two-dimensional pessimistic section may not be intuitively obvious.…”

Upper-Bound Multi-Rigid-Block Solutions for Seismic Performance of Slopes with a Weak Thin Layer

“…This characteristic requires special attention from engineers with regard to the low shear strength of the weak layer, which has an adverse influence on the performance of slopes. Varying methodologies have been employed to estimate the static stability of slopes with a thin layer, including the limit equilibrium method (Fredlund and Krahn [1]), the upper-bound solution method (Huang and Song [2]), and finite element analysis (Griffiths and Marquez [3]; Ho [4]). However, few studies have focused on the seismic stability of nonhomogeneous slopes.…”